EDIT: I rolled a critical fail in reading comprehension and I thought the other track was N per integer instead of 1 per real number in the previous version of this comment.

The people in the real number track are already dead by the time the trolley arrives due to the forces involved in cramming them so tightly together. I.e. they are basically just a gore pile the moment after the people are somehow arranged like that.

I pick the real number track so that no one new has to die.

I am sure even countably infinite people would violate some law of thermodynamics.

I actually would like to choose the track where the number of people increases by one (so 1, 2, 3, 4...) and then the train will kill -1/12 people

PS Yes, I know this sum result is problematic, it's only a joke

Pull it -1/12 of the way, causing the infinity to converge to a real number.

I quickly carry the people to the other side so they all can get run over.

build new tracks to make the trolley run on (possibly in circles).

Slip the switch, like always

The existence of the bottom track would imply an infinite density of people, which would create a black hole and kill everyone involved, regardless of the trolley's presence

Do nothing - maximum destruction

Is it possible to get this thing to skid on both rails? You'll only be killing an infinite number of people anyway.

I have a tangential question I have been wanted an explanation for:

If there are infinite universes, would there be infinite earth's?

I remember (an) answer is infinite universes doesn't necessarily mean infinite earth's. A cool analogy of a CD rack was used when I read it, but I can't find it. Does anyone else have an explanation and/or analogy for this?

Since there's an infinite number of people to kill in either case I can just do nothing, and thus by inaction most of those infinite people will have more than enough time for someone else to rescue them. Maybe the State, that's what they're there for.

Probably pull the leaver cuz then I can jump in front of the train.